An Archibald Prize finalist and two of her sons, charged over the murder of an 81-year-old Canberra woman, are facing delays in their case as lawyers clashed over the case in the ACT Magistrates Court.

Melissa Beowulf, 60, and her sons Thorsten, 31, and Bjorn, 29, are accused of killing Katherine Panin in 2015.

Ms Panin, who was Ms Beowulf's mother-in-law and the grandmother of her sons, was found injured at the base of some stairs and later died.

The three have been in jail since August.

But today prosecutors refused to agree to commit them to trial in the ACT Supreme Court, saying they needed more time and asking for a date in January.

Lawyers for the trio objected, and Magistrate Robert Cook queried why the case could not proceed.

"The question is why someone is in custody for five months and then not even committed," he said.

"I do not understand."

Prosecutor Margaret Jones told the court more time was needed to gather financial documents.

But a lawyer for Ms Beowulf, Rachel Bird, objected and told the court there had already been a 15-month investigation that included a search of the family home for financial documents.

Lawyer for the two sons, Louise Taylor, also complained, saying: "It's appropriate some pressure be brought to bear on the director's office."

Mr Cook refused to list the case in January, but has set the matter down for later this month, when he said there would be a potential committal.

In the meantime, he has urged both sides to keep the discussion going.